Kink networks for scalar fields in dimension 1+1.

Abstract: Consider a real scalar wave equation in dimension 1+1 with a positive  external potential having non-degenerate isolated zeros. I will speak about the problem of construction of weakly interacting pure multi-solitons, that is solutions converging exponentially in time to a superposition of Lorentz-transformed solitons (“kinks”), in the case of distinct velocities. In a joint work with Gong Chen from the University of Toronto, we prove that these solutions form a 2K-dimensional smooth manifold in the space of solutions, where K is the number of the kinks.

This manifold is invariant under the transformations corresponding to the invariances of the equation, that is space-time translations and Lorentz boosts.

Posted on May 25, 2021 in Differential Equations, Seminars